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Erscheinungsjahr: 
2025
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[Journal:] Games [ISSN:] 2073-4336 [Volume:] 16 [Issue:] 2 [Article No.:] 12 [Year:] 2025 [Pages:] 1-37
Verlag: 
MDPI, Basel
Zusammenfassung: 
We consider a dynamic game with asymmetric information where each player privately observes a noisy version of a (hidden) state of the world V, resulting in dependent private observations. We study the structured perfect Bayesian equilibria (PBEs) that use private beliefs in their strategies as sufficient statistics for summarizing their observation history. The main difficulty in finding the appropriate sufficient statistic (state) for the structured strategies arises from the fact that players need to construct (private) beliefs on other players' private beliefs on V, which, in turn, would imply that one needs to construct an infinite hierarchy of beliefs, thus rendering the problem unsolvable. We show that this is not the case: each player’s belief on other players' beliefs on V can be characterized by her own belief on V and some appropriately defined public belief. We then specialize this setting to the case of a Linear Quadratic Gaussian (LQG) non-zero-sum game, and we characterize structured PBEs with linear strategies that can be found through a backward/forward algorithm akin to dynamic programming for the standard LQG control problem. Unlike the standard LQG problem, however, some of the required quantities for the Kalman filter are observation-dependent and, thus, cannot be evaluated offline through a forward recursion.
Schlagwörter: 
dynamic games with asymmetric information
perfect Bayesian equilibrium (PBE)
structured equilibria
Linear Quadratic Gaussian (LQG) games
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